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## Homework Statement

A point moves with constant speed (value) over a sphere, following the curve defined by: f = t = l

For t=0, the point is at (t,f) = (0,0) and for t=3 it's at (pi/4, pi/4).

How long does it take to reach the north pole of the sphere?

## Homework Equations

The parametric equations for this sphere are:

x = 5·cos f·cos t

y = 5·cos f·sin t

z = 5·sin f

## The Attempt at a Solution

OK first of all, the parametric equations turn into:

x = 5·cos

^{2}l

y = 5·cos l·sin l

z = 5·sin l

Then we know that:

v

^{2}= x'

^{2}+ y'

^{2}+ z'

^{2}

So we find:

x' = -5·sin(2l)

y' = 5·cos(2l)

z' = 5·cos l

By adding them up, we simplify the squared sines-cosines:

v

^{2}= 25(1 + ·cos

^{2}l)·(dl/dt)

^{2}

v·dt = 5√(1 + ·cos

^{2}l)·dl

However I don't know how to find v, and I'm not sure this is correct so far.

Thank you for your help